"She deserved it," Harry said, breathing very fast. "She deserved what she got. You keep away from me." (2.3.30)
Harry issues a rather harsh judgment against Aunt Marge here, and it's notably a judgment borne out of anger. The detail about Harry's quick breathing reveals just how agitated he is.
Hagrid wasn't a fully qualified wizard; he had been expelled from Hogwarts in his third year for a crime he had not committed. It had been Harry, Ron, and Hermione who had cleared Hagrid's name last year. (5.264)
The justice system in the wizarding world has definite flaws – it's an idea that got introduced in the second book, and we definitely learn more about it here.
"Miss Dursley has been punctured and her memory has been modified. She has no recollection of the incident at all. So that's that, and no harm done."
Fudge smiled at Harry over the rim of his teacup, rather like an uncle surveying a favorite nephew. Harry, who couldn't believe his ears, opened his mouth to speak, couldn't think of anything to say, and closed it again. (3.122-3)
Harry gets a crash course in politics here, as Fudge opts to not punish him for a variety of reasons, none of which have to do with actual rules or laws.
"Five points from Gryffindor," said Snape, which wiped the smile from every face. "I told you not to help him, Miss Granger. Class dismissed." (7.1.62)
Snape might be the most unfair teacher of all time and scenes with him usually reveal a lot of anger and frustration in his students/victims.
Malfoy let out a low, sneering laugh.
"Maybe you'd rather not risk your neck," he said. "Want to leave it to the Dementors, do you? But if it was me, I'd want revenge. I'd hunt him down myself." (7.1.54)
Malfoy is a little punk, and his spiel about vigilante justice is definitely ironic, considering how much of a coward he is (see how he quits bullying Harry the second a teacher like Lupin appears, or how he rushes off after Hermione hits him, not willing to risk an actual all-out fight with her).
The map was one of those dangerous magical objects Mr. Weasley had been warning him against [...] but then, Harry reasoned, he only wanted to use it to get into Hogsmeade, it wasn't as though he wanted to steal anything or attack anyone [...] and Fred and George had been using years without anything horrible happening [...] (10.3.52)
Harry's judgment is definitely biased here. Stylistically, we get a series of clauses where Harry tries to convince himself that using the Map is OK. The clauses emphasize how quickly Harry is thinking and how desperate he is to justify his decision to use the Map.
Did he realize he was facing twelve years in Azkaban, twelve years that would make him unrecognizable?
But the Dementors don't affect him, Harry thought, staring into the handsome, laughing face. He doesn't have to hear my mum screaming if they get too close–. (11.1.5-6)
It's interesting that Harry feels some compassion at first for the happy young man in the picture, before remembering what he heard about how Black is holding up freakishly well in prison. Harry concludes that Black isn't being punished enough since Harry is still suffering.
"Don't be silly," said Hermione, in a panicky voice. "Harry doesn't want to kill anyone, do you, Harry?"
Again, Harry didn't answer. He didn't know what he wanted to do, All he knew was that the idea of doing nothing, while Black was at liberty, was almost more than he could stand." (11.2.19-20)
Harry definitely has to deal with a major moral dilemma after learning what he thinks is the truth about Black. Should he avenge his parents' death or not? Though the answer to that is definitely no (or this book series would have taken a very odd turn), but reaching that conclusion is a definite struggle for Harry. See the scene where he freezes when trying to kill Sirius.
He had forgotten about magic – he had forgotten that he was short and skinny and thirteen, whereas Black was a tall, full-grown man – all Harry could think was that he wanted to hurt Black as badly as he could and that he didn't care how much he got hurt in return –. (17.88)
It's fitting that this scene, in which Harry is consumed by anger, focuses so much on forgetting. His entire world has boiled down to the desire to hurt Black.
Professor Snape is here at school with us. [...] Sirius here played a trick on him which nearly killed him, a trick which involved me –"
Black made a derisive noise.
"It served him right," he sneered. "Sneaking around, trying to find out what we were up to [...] hoping he could get us expelled [...]" (18.55-7)
Sirius's idea of justice could use some adjustment. It's really interesting that he says essentially the same thing about Snape as he later does about Peter. He has nothing but contempt for people who "sneak" around and try to cause problems for others.
"See here, Snape, be reasonable," said Fudge. "This door's been locked, we just saw –"
"THEY HELPED HIM ESCAPE, I KNOW IT!" Snape howled, pointing at Harry and Hermione. His face was twisted; spit was flying from his mouth.
It's fitting that Snape gets a taste of his own medicine here. He's usually horribly unfair to everyone else, so it's fitting that he gets to experience an unfair situation too, where he basically gets screwed over.
Black and Lupin were looking at each other. Then, with one movement, they lowered their wands.
"You're the only person who has the right to decide, Harry," said Black. "But think [...] think what he did [...]"
"He can go to Azkaban," Harry repeated. "If anyone deserves that place, he does [...]" (19.175-7)
Harry's phrasing here is very interesting. He refers to Azkaban as "that place," implying that it's truly awful. But he decides that Peter really does deserve it, even if no one else really does.